{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a74c33cd",
   "metadata": {},
   "source": [
    "# 反因果零相位滤波器的实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4cca0e0",
   "metadata": {},
   "source": [
    "在FIR滤波器的情况下，可以设计线性相位滤波器，当应用于数据时（使用filter/lfilter或conv/convolve），只需将输出延迟固定数量的采样。然而，对于IIR滤波器，相位失真通常是高度非线性的。filtfilt函数使用当前点前后信号中的信息，本质上是“看到未来”，以消除相位失真"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05ec6bf8",
   "metadata": {},
   "source": [
    "要了解filtfilt是如何做到这一点的，回想一下，如果实序列$x(n)$的Z变换是$X(z)$，那么时间反转序列$x(-n)$的Z变换就是$X(z^{-1})$。考虑下面的处理方案："
   ]
  },
  {
   "attachments": {
    "image.png": {
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    }
   },
   "cell_type": "markdown",
   "id": "8844ec10",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dad1cef8",
   "metadata": {},
   "source": [
    "当$|z|=1$，其中$z=e^{j\\omega}$，此时输出减少到$X(e^{j\\omega}){\\left|H(e^{j\\omega})\\right|}^2$。给定序列$x(n)$的所有样本，可以得到具有零相位失真的双滤波版本的x。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a272bdc1",
   "metadata": {},
   "source": [
    "例如，以100Hz采样的1秒持续时间信号，由3Hz和40Hz的两个正弦分量组成，是"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f8123346",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "from scipy import signal \n",
    "import matplotlib.pyplot as plt  \n",
    "\n",
    "fs = 100 \n",
    "t = np.arange(0,1+1/fs,1/fs) \n",
    "x = np.sin(2*np.pi*t*3)+0.25*np.sin(2*np.pi*t*40)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f513bb2",
   "metadata": {},
   "source": [
    "现在创建一个6阶巴特沃斯低通滤波器来滤除高频正弦波。使用**filter/lfilter**和**filtfilt**进行比较的过滤器x："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ac5730d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x151ff5d7700>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "b,a = signal.butter(6,20/(fs/2))  \n",
    "\n",
    "y = signal.filtfilt(b,a,x) \n",
    "zi = signal.lfilter_zi(b,a)*0 \n",
    "yy = signal.lfilter(b,a,x)  \n",
    "\n",
    "fig,ax = plt.subplots() \n",
    "ax.plot(t,x,t,y,t,yy) \n",
    "ax.legend(['Original','filtfilt','filter'],loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ee8f8d4",
   "metadata": {},
   "source": [
    "两种滤波版本都消除了原始信号中明显的40 Hz正弦波。该图还显示了**filter**和**filtfilt**的区别。**filtfilt**线与原来的3 Hz正弦波同相，而**filter/lfilter**线延迟。**filter/lfilter**线在早期显示瞬态。**filtfilt**通过仔细选择初始条件，并在输入序列上预加一个短的、反射的输入序列片段，来减少滤波器启动瞬变。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70fb2d80",
   "metadata": {},
   "source": [
    "为了获得最佳效果，请确保要滤波的序列的长度至少是滤波器序列的三倍，并且在信号两边逐渐变为零。"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
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